Interpolation of quasi noncommutative $L_p$-spaces

Abstract

Let $\mathcal{M}$ be a ($\sigma$-finite) von Neumann algebra associated with a normal faithful state $\varphi .$ We prove a complex interpolation result for a couple of two (quasi) Haagerup noncommutative $L_p$-spaces $L_{p_0}(\mathcal{M},\varphi )$ and $L_{p_1}(\mathcal{M},\varphi ),0<p_0<p_1\le \infty ,$ which has further applications to the sandwiched $p$-Rényi divergence.

arXiv comment26 pages

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Cited by in corpus (2)

• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Relative entropy for von Neumann subalgebras